LIE COALGEBRAS AND RATIONAL HOMOTOPY THEORY II: HOPF INVARIANTS


Sinha D., Walter B.

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.365, no.2, pp.861-883, 2013 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 365 Issue: 2
  • Publication Date: 2013
  • Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.861-883
  • Keywords: Hopf invariants, Lie coalgebras, rational homotopy theory, graph cohomology

Abstract

We develop a new framework which resolves the homotopy periods problem. We start with integer-valued homotopy periods defined explicitly from the classic bar construction. We then work rationally, where we use the Lie coalgebraic bar construction to get a sharp model for Hom(pi*X,Q) for simply connected X. We establish geometric interpretations of these homotopy periods, to go along with the good formal properties coming from the Koszul-Moore duality framework. We give calculations, applications, and relationships with the numerous previous approaches.